Question

Which one of the following statements expresses a true proportion? A. 2:1 = 1:2 B. 7:9 = 8:9 C. 54:9 = 6:3 D. 3:4 = 9:12

Answer 1

$A:\\2:1=\frac{2}{1};\ 1:2=\frac{1}{2}\\\\2:1=1:2\to\frac{2}{1}=\frac{1}{2}\to cross\ multiply\\to (2)(2)=(1)(1)\to 4=1\ FALSE!!! :( \\=====================================$

$B:\\7:9=\frac{7}{9};\ 8:9=\frac{8}{9}\\\\7:9=8:9\to\frac{7}{9}=\frac{8}{9}\ only\ if\ 7=8\ FALSE!!!\ :( \\=====================================$

$C:\\54:9=\frac{54}{9}=6;\ 6:3=\frac{6}{3}=2\\\\54:9=6:3\to6=2\ FALSE!!!\ :(\\=====================================$

$D:\\3:4=\frac{3}{4};\ 9:12=\frac{9}{12}=\frac{9:3}{12:3}=\frac{3}{4}\\\\3:4=9:12\to\frac{3}{4}=\frac{3}{4}\ CORRECT\ :)\\=====================================\\\\\huge\boxed{Answer:\boxed{D}}}$